"Emergent Criticality and Friedan Scaling in a 2D Frustrated Heisenberg
Antiferromagnet"
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In most systems that exhibit order at low temperatures, the order occurs in the
elementary degrees of freedom such as spin or charge. Prominent examples are
magnetic or superconducting states of matter. In contrast, emergent order
describes the phenomenon where composite objects exhibit longer range
correlations. Such emergent order has been suspected to occur in a range of
correlated materials. One specific example are spin systems with competing
interactions, where long-range discrete order in the relative orientation of
spins may occur. Interestingly, this order parameter may induce other phase
transitions as is the case for the nematic transition in the iron pnictides. In
this talk, we introduce and discuss a system with emergent Z6 symmetry, a
two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice
consisting of interpenetrating honeycomb and triangular lattices [1,2]. The
multiple spin stiffnesses can be captured in terms of a four-dimensional metric
tensor, and the renormalization group flow of the stiffnesses is described by
the Ricci flow of the metric tensor. The key result is a decoupling of an
emergent collective degree of freedom given by the relative phase of spins on
different sublattices. In particular, our results reveal a sequence of two
Berezinskii-Kosterlitz-Thouless phase transitions that bracket a critical phase.
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[1] P. P. Orth, P. Chandra, P. Coleman, J. Schmalian, Phys. Rev. Lett. 109,
237205 (2012).
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[2] P. P. Orth, P. Chandra, P. Coleman, J. Schmalian, Phys. Rev. B 89, 094417
(2014).